发表机构
Department of Mathematics and Statistics, Université Laval（拉瓦尔大学数学与统计系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对聚类圆形响应问题，提出广义角回归的简约混合效应扩展模型，结合圆形随机截距与标量随机斜率，建立相关理论和框架，经模拟研究与实际应用验证了模型的有效性及方差分量推断的实用性。
AI 中文摘要
在重复定向实验、运动生态学和传感器研究中会出现聚类圆形响应，其中方向性和聚类内依赖性都很重要。我们提出了广义角回归的一种简约混合效应扩展，其中平均方向由二维共识向量的方向定义。该模型将冯·米塞斯圆形随机截距与作用于一个共识向量系数的预先指定的高斯标量随机斜率相结合。在标量斜率条件下，圆形截距可进行解析积分，产生一维边际似然并避免一般随机斜率模型所需的高维积分。我们建立了高级设计条件可识别性条件、远离方差边界的聚类渐近似然理论以及确定性求积、诊断和模型评估的实用框架。模拟研究调查了数值稳定性和有限样本性能。对重复的沙蚤定向数据的应用说明了所提出的方法，并突出了方差分量推断的实际考虑因素。
英文摘要
Repeated directional responses may vary between individuals in both overall orientation and sensitivity to explanatory cues. We study homogeneous angular regression with correlated Gaussian cue coefficients and a circular random intercept, separating observation concentration from resultant length. Constructive identification conditions recover the joint coefficient law, intercept concentration and observation-error parameters, including unknown uniform contamination. The argument combines repeated contrasts, an arc-support restriction and joint Fourier deconvolution, and extends to exogenous continuous designs. Integration in coefficient coordinates yields smooth population scores even when resultant cancellation prevents a regular latent mode. A fixed-proposal adaptive importance algorithm evaluates the marginal likelihood and its derivatives. In 8,000 independent simulated datasets, 7,998 fits pass numerical checks, and 12,799 of 12,800 local profile intervals are available. Correlation profile-set coverage nevertheless ranges from 91.9% to 94.8% at the nominal 95% level. Greater precision and numerical availability therefore do not ensure calibrated inference. An exploratory extension to 150 Canadian weather stations is evaluated on 259,807 three-hour forecasts from a new 2026 period after fitting on 2023-2025 data. With circular station rotations in all matched models, independent station slopes give modest predictive gains over slopes shared within regions, in all five regions. Estimating their correlations adds no useful predictive gain; this does not assess parameter uncertainty, and predictive calibration remains imperfect. The application uses a noncancelling mean and Laplace integration, so it illustrates the model class rather than testing the proposed algorithm.
Comments23 pages, 6 figures, 4 tables; 55-page supplementary material. Substantially revised: new title, expanded identifiability results and numerical assessment, and a 150-station Canadian wind application
